[Mastermander]

1.\[
\left| {\frac{1}{2} - \frac{1}{{\sqrt 2 }}} \right| - \left| {2 - \sqrt 2 } \right|
\]
\[
\because\, \frac{1}{2} - \frac{{\sqrt 2 }}{2} < 0
\]
\[
\frac{{\sqrt 2 }}{2} - \frac{1}{2} - 2 + \sqrt 2 = \frac{{3\sqrt 2 }}{2} - \frac{5}{2}
\]
2.\[
\frac{{8^{\frac{2}{3}} }}{{\sqrt[4]{{144}}}} \cdot \frac{{18^{\frac{1}{2}} }}{{\sqrt 6 }} = \frac{4}{{\sqrt {12} }} \cdot \frac{{3\sqrt 2 }}{{\sqrt 3 \sqrt 2 }} = \frac{{12}}{6} = 2
\]
3.\[
\left( {1 - \sqrt 2 } \right)^2 \left( {2 + \sqrt 8 } \right)^2 \left( {1 + \sqrt 2 } \right)^3 \left( {2 - \sqrt 8 } \right)^3
\]
\[
\left[ {\left( {1 - \sqrt 2 } \right)^2 \left( {1 + \sqrt 2 } \right)^2 } \right]\left[ {\left( {2 + \sqrt 8 } \right)^2 \left( {2 - \sqrt 8 } \right)^2 } \right]\left( {1 + \sqrt 2 } \right)\left( {2 - \sqrt 8 } \right)
\]
\[
\left( { - 1} \right)^2 \left( {4 - 8} \right)^2 \left( {1 + \sqrt 2 } \right)\left( {1 - \sqrt 2 } \right)2 = 32\left( { - 1} \right) = - 32
\]
4.\[
x \le 5 \to x\left| x \right| \le 25
\]
5.\[
\left( {3 + \frac{3}{8}} \right)^{3x} = \frac{{16}}{{81}}
\]
\[
\left( {\frac{{27}}{8}} \right)^{3x} = \left( {\frac{2}{3}} \right)^4
\]
\[
\left( {\frac{2}{3}} \right)^{ - 9x} = \left( {\frac{2}{3}} \right)^4
\]
\[
x = - \frac{4}{9}
\]

6. ให้อีกรากหนึ่งเป็น b จะได้ว่า
\[
- \frac{1}{2}b = - \frac{1}{a} \to \quad \frac{b}{2} = \frac{1}{a}
\]
\[
b - \frac{1}{2} = - \frac{3}{a}=-\frac{3b}{2}
\]
\[
b = \frac{1}{5}
\]
7.\[
n\left( {A \cap B} \right) = 88 - 76 = 12
\]
\[
n\left( {A \cup B} \right) = n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right)
\]
\[
88 = 45 + n\left( B \right) - 12
\]
\[
n\left( B \right) = 55
\]
8.\[
39 + 19 - 46 = 12
\]
9. ตอบ 10\[
r=\{\left( {1,1} \right),\left( {1,2} \right),\left( {1,3} \right),\left( {1,4} \right),\left( {2,2} \right),\left( {2,3} \right),\left( {2,4} \right),\left( {3,3} \right),\left( {3,4} \right),\left( {4,4} \right)\}\]
10.\[
a = \frac{{5 - 1}}{2} = 2
\]

11. วาดรูปเอา...ตอบ $4\sqrt3$

12.\[
a_n = a_1 + \left( {n - 1} \right)d
\]
\[
a_1 + 29d - \left( {a_1 + 9d} \right) = 30
\]
\[
d = \frac{3}{2} = 1.5
\]
13. ตอบ 1

14. \[
\frac{1}{{10}}
\]
15.\[
Q_3 = \# 15\quad ,\;P_{45} = \# 9
\]
\[
23 - 18 = 5
\]

16.\[
\bar X = \frac{{1\left( {2.5} \right) + 1.5\left( 3 \right) + 1\left( {3.5} \right) + 1.5\left( 2 \right)}}{{1 + 1.5 + 1 + 1.5}} = 2.70
\]
17. 3:2\[
\bar X = \frac{{N_1 \bar x_1 + N_2 \bar x_2 }}{{N_1 + N_2 }}
\]
\[
31\left( {N_1 + N_2 } \right) = 35N_1 + 25N_2
\]
\[
4N_1 = 6N_2
\]
\[
\frac{{N_1 }}{{N_2 }} = \frac{6}{4} = \frac{3}{2}
\]
18.\[
\bar y = 2\bar x - 30
\]
\[
\bar x = \frac{{31 + 34 + 35 + 36 + 39}}{5} = \frac{{175}}{5} = 35
\]
\[
\bar y = 2\left( {35} \right) - 30 = 40
\]
19.\[
\bar X = \frac{{3\left( 4 \right) + 8\left( 9 \right) + 13\left( 2 \right) + 18\left( 5 \right)}}{{4 + 9 + 2 + 5}} = \frac{{200}}{{20}} = 10
\]
20.\[
3,x,6,6,10\quad ;\;Med = 6
\]
\[
\frac{{3 + x + 6 + 6 + 10}}{5} = 6
\]
\[
x = 5
\]